Recent content by BifSlamkovich

x_n = [(−1)^n] * [1-{1/n}] Each side of 0 is going to contain x_n for infinitely many x_n's, supposedly. But does it really, because I thought infinitely many x_n's meant for all x_n's?

Suppose that closed intervals I_0 ⊃ I_1⊃ ... ⊃ I_m and natural numbers n1 < n2 < ... < nm have been chosen such that for each 0 ≤ k ≤ m, (2) |Ik| = b−a/2k, x_{n}_{k}∈Ikn and xn ∈ Ik for infinitely many n. So, in trying to apply the above proof to this particular sequence, when we choose...

How does this theorem apply to the sequence: x_{n} = (-1)^{n} * 1-1/n?

It seems that I do not understand the notation for the statement: x_{n} \in I_{k} for inifinitely many n. Does it mean x_{1}, x_{2}, x_{3}, x_{4} have to all be in the chosen interval?

Homework Statement Every bounded sequence has a convergent subsequence. Homework Equations Suppose that closed intervals I_0 \supset I_1\supset ... \supset I_m and natural numbers n_{1} < n_{2} < ... < n_{m} have been chosen such that for each 0 \leq k \leq m, (2) |I_{k}| =...

Squaring the deviation emphasizes larger differences. Additionally, for a normal distribution, 68% of values lie with 1 standard deviation of the mean, 95% of values lie within 2 standard deviations of the mean, and 99.7% of the values lie within 3 standard deviations of the mean. For some...

Checking this fact and the basic idea of modeling ordered pairs with sets.

Please explain the logic, as this is the definition provided by the book I am referring to.

Yes.

Suppose there are n pictures and n words. Each word matches with exactly one out of the n pictures. What is the probability function of having exactly y words match up correctly?

Homework Statement dy/dx = (6x^(2)+xy+6y^(2))/(x^2) Homework Equations v = y/x y' = v + xv' The Attempt at a Solution y' = tan(6ln(abs(x))-C)/x ===> apparently not correct

In the ordinary least squares procedure I have obtained an expression for the sum of squared residuals, S, and then took the partial derivatives of it wrt β0 and β1. Help me to condense it into the matrix, -2X'y + 2X'Xb. ∂S/∂β0 = -2y1x11 + 2x11(β0x11 + β1x12) + ... + -2ynxn1 + 2xn1(β0xn1 +...

Sorry about not posting the problem statement in the main text. And I double-posted because it was first in the wrong category. This is calc., not pre-calc.

1. Homework Statement x g(x) g'(x) -2 -2 2 -1 0 1 0 1 2 1 3 4 2 7 3 3 9 2 2. Homework Equations chain rule 3. The Attempt at a Solution differentiate (2/x) and multiply that times g'(2/x). Plug in 2/3 into -2/(x^2), and one obtains -9/2. g'(2/((2/3)))= 2. The two...

f(1) + cg(1) from the left side has to equal f(1) + cg(1) from the right side in order for the lim x-> 1 to exist, i.e., an appropriate value of c has to be determined. But idk if it's the very same value that makes the function, f(1) + cg(1), continuous at x=1, because continuity has 3...